Logic and Philosophy of Logic, Misc

Philosophy of logic faces a paradox that no major position in the field has satisfactorily resolved: logic appears to be both unconditionally normatively binding on any rational agent and genuinely revisable through rational inquiry. Every attempt to resolve this paradox within the dominant tradition has failed, and this paper argues that the failures share a common structural source. The top-down model, reflective equilibrium approaches, and anti-exceptionalism all embed what I call the Single-Dimension Assumption (SDA): the presupposition that logical normativity and (...) logical revisability compete on a single axis such that strengthening one necessarily weakens the other. The Two-Dimensional resolution replaces the SDA: constitutive authority and regulative adequacy are orthogonal dimensions answering different questions, and the paradox dissolves once they are separated. Two original arguments, the Mechanism Problem and Adoption Problem, establish that the top-down model fails because it attempts to derive constitutive authority from regulative principles. After establishing both original arguments, the paper turns to Steinberger tripartite analysis as independent convergent confirmation. A detailed case study of universal instantiation demonstrates the abstract conclusions concretely. (shrink)

Grice argues that indicative conditionals ‘if p then q’ have conventional, truth conditional meaning according to the material conditional ‘p  q’. In order to explain away the known paradoxes with this interpretation, he distinguishes between truth conditions and assertion conditions, attempting to demonstrate that the assumed connection between ‘p’ and ‘q’ (the Indirectness Condition) is a conversational implicature; hence a matter only relevant for the assertion conditions of a conditional. This paper argues that Grice fails to demonstrate i) that (...) the Indirectness Condition is cancellable, hence a conversational implicature, ii) that the Indirectness Condition is not part of the conventional, truth-relevant meaning of ‘if’, and accordingly, iii) semantic or logical equivalence between indicative and material conditionals. (shrink)

The material interpretation of conditionals is commonly recognized as involving some paradoxical results. I here argue that the truth functional approach to natural language is the reason for the inadequacy of this material interpretation, since the truth or falsity of some pair of statements ‘p’ and ‘q’ cannot per se be decisive for the truth or falsity of a conditional relation ‘if p then q’. This inadequacy also affects the ability of the overall formal system to establish whether or not (...) arguments involving conditionals are valid. I also demonstrate that the Paradox of Indicative Conditionals does not actually involve a paradox, but instead contains some paralogistic elements that make it appear to be a paradox. The discussion of the paradox in this paper further reveals that the material interpretation of conditionals adversely affects the treatment of disjunctions. Much has been said about these matters in the literature that point in the same direction. However, there seems to be some reluctance against fully complying with the arguments against the truth functional account of conditionals, since many of the alternative accounts rely on the material conditional, or at least on an understanding of the conditional as a function of antecedent and consequent in a similar sense as the material conditional. My argument against truth functionality indicates that it may in general involve similar problems to treat conditionals as such functions, whether one deals with theories of truth, assertability or probability. (shrink)

The conditional interpretation of general categorical statements like ‘All men are animals’ as universally quantified material conditionals ‘For all x, if x is F, then x is G’ suggests that the logical structure of law statements is conditional rather than categorical. Disregarding the problem that the universally quantified material conditional is trivially true whenever there are no xs that are F, there are some reasons to be sceptical of Frege’s equivalence between categorical and conditional expressions. Now many philosophers will claim (...) that the material conditional interpretation of laws statements, dispositions ascriptions, or any causal claim is generally accepted as wrong and outdated. Still, there seem to be some basic logical assumptions that are shared by most of the participants in the debate on causal matters which at least stems from the traditional truth functional interpretation of conditionals. This is indicated by the vocabulary in the philosophical debate on causation, where one often speaks of ‘counterfactuals’, ‘possible worlds’ and ‘necessity’ without being explicit on whether or to what extent one accepts the logical-technical definition of these notions. To guarantee a non-Humean and non-extensional approach to causal relations, it is therefore important to be aware of the logical and metaphysical implications of the technical vocabulary. In this paper we want to show why extensional logic cannot deal with causal relations. Via a logical analysis of law-like statements ‘All Fs are Gs’ we hope to throw some new light on interrelated notions like causation, laws, induction, hypotheticality and modality. If successful, our analysis should be of relevance for a deeper understanding of any type of causal relations, whether we understand them to be laws, dispositions, singulars or categoricals. (shrink)

Homo deceptus is a book that brings together new ideas on language, consciousness and physics into a comprehensive theory that unifies science and philosophy in a different kind of Theory of Everything. The subject of how we are to make sense of the world is addressed in a structured and ordered manner, which starts with a recognition that scientific truths are constructed within a linguistic framework. The author argues that an epistemic foundation of natural language must be understood before laying (...) claim to any notion of reality. This foundation begins with Ludwig Wittgenstein’s Tractatus Logico-Philosophicus and the relationship of language to formal logic. Ultimately, we arrive at an answer to the question of why people believe the things they do. This is effectively a modification of Alfred Tarski’s semantic theory of truth. The second major issue addressed is the ‘dreaded’ Hard Problem of Consciousness as first stated by David Chalmers in 1995. The solution is found in the unification of consciousness, information theory and notions of physicalism. The physical world is shown to be an isomorphic representation of the phenomenological conscious experience. New concepts in understanding how language operates help to explain why this relationship has been so difficult to appreciate. The inclusion of concepts from information theory shows how a digital mechanics resolves heretofore conflicting theories in physics, cognitive science and linguistics. Scientific orthodoxy is supported, but viewed in a different light. Mainstream science is not challenged, but findings are interpreted in a manner that unifies consciousness without contradiction. Digital mechanics and formal systems of logic play central roles in combining language, consciousness and the physical world into a unified theory where all can be understood within a single consistent framework. (shrink)

This paper argues that mathematics cannot be regarded as either a mere invention or a purely hypothetico-deductive enterprise. By extending Goodman’s “grue” problem into the mathematical domain, it is shown that definitional interequivalence between predicates does not preserve epistemic properties such as decidability. Even when two predicates are formally interdefinable, only one may be epistemically admissible within a consistent formal system. This constraint reveals that mathematical language is not a free invention but is shaped by deeper semantic and computational necessities. (...) Mathematics thus occupies a unique epistemological position: it is a discipline in which formal equivalence does not entail epistemic equivalence, and where the very possibility of truth and knowledge is conditioned by the structure of the system itself. (shrink)

We present a philosophical motivation for the logics of formal inconsistency, a family of paraconsistent logics whose distinctive feature is that of having resources for expressing the notion of consistency within the object language. We shall defend the view according to which logics of formal inconsistency are theories of logical consequence of normative and epistemic character. This approach not only allows us to make inferences in the presence of contradictions, but offers a philosophically acceptable account of paraconsistency.

This paper explores the paradoxical claim “This article is not written by helping AI.” On the one hand, if AI contributes to the drafting process, the claim appears false. On the other hand, if authorship requires semantic intention and responsibility, then the claim may be true even when AI generates text. Drawing on Searle’s Chinese Room, Tarski’s theory of truth, and debates on authorship in philosophy of language, I argue that authorship requires intentionality and responsibility, which AI systems lack. The (...) paradox is resolved by distinguishing between syntactic production and semantic authorship. AI can assist in generating words, but authorship remains a human act of responsibility. -/- (This article is distinctive in nature, and its central problem is: who is the author?) Farzad Didehvar provided an AI system with only a single phrase in Persian, which translates into English as: “This article is not written by Helping AI.” From that seed, the AI generated a complete article in English. The article itself argues—semantically—that it was not written by an AI tool. At the same time, it was not literally written by Farzad either, since he only supplied the initial phrase. This raises a paradoxical question: if the article is neither authored by the AI nor by the human, then who is the true writer? An answer will be provided in the next article, but the author is interested in hearing other opinions. (shrink)

ECONOMIST: I study the rational pursuit of ends. What do you think of the relation between the rational pursuit of ends and logic is? LOGICIAN: I don't know. I just prioritise logic. If someone asks me, does a conclusion follow from certain premises, I tell them the answer (as I believe it to be). I don't think: it is rational for my aim(s) in life to fail here, so I will. And I don't think: it is rational for me to (...) get myself into a state in which I am inwardly less logical, so I will. ECONOMIST: But surely you must make exceptions to your policy. LOGICIAN: This approach is too complicated for me, making exceptions in abnormal circumstances. But my body might intervene in some circumstances: I might pass out. FRESHSTILL1: My body is affected too, but I am much more sensitive than you are. My battery runs out so quickly. FRESHSTILL2: If I feel something slightly off in my body (and I attend to these things much more than you), then I interpret what is going on until I feel better. POSTMODERN PSYCHOANALYST: Freud and others tried to interpret the symptom, believing that when they got the correct interpretation it would go away. But the body is just not coherent. One symptom requires X and another symptom requires not-X. VALUEPOO: You have to prioritise doing well-formed poo, as depicted on bus stands in Manchester during Coronavirus season. MADMAN: A desk is your mother. A desk is your mother. A desk is your mother. PSYCHIATRIST: Okay, point taken! (shrink)

Forthcoming in Darren Bradley (ed.), Carnap and Contemporary Philosophy. -/- This paper is centered on Carnap’s views on rationality. More specifically, much of the focus is on a puzzle regarding Carnap’s view on rationality that Florian Steinberger has recently discussed. Not only is Steinberger’s discussion of significant intrinsic interest: his discussion also raises general questions about Carnap interpretation. As I have discussed in earlier work, there are two very different ways of interpreting Carnap’s talk of “frameworks” – and, relatedly, different (...) ways of interpreting Carnap’s principle of tolerance. Carnap can be interpreted as either a relativist or as what I call a language pluralist. Steinberger’s puzzle arises given the relativist interpretation; I believe the language pluralist interpretation is correct. Most of the discussion will concern the correct interpretation of Carnap, and what this means for Steinberger’s puzzle. While I will not here mount a full defense of the language pluralist interpretation, I will pause to discuss Vera Flocke’s recent criticism of it. Towards the end, I will describe a puzzle regarding rationality different from Steinberger’s. The puzzle that I describe does arise already for the language pluralist. (shrink)

This article presents the basic foundations for supporting formal languages with syntax that admits indiscernible signs. We present their ontological motivation, derived from the non-identity entities of quantum mechanics, and their basic formalism. A possible semantics for interpreting such signs is shown, using the theory of quasi-sets without atoms Q−. -/- Este artículo presenta los fundamentos básicos para sostener los lenguajes for males con sintaxis que admitan signos indiscernibles. Presentamos su motivación ontológica, proveniente de los entes sin identidad de la (...) mecánica cuántica, y su formalismo básico. Se muestra una posible semántica para interpretar tales signos utilizando la teoría de casi-conjuntos sin átomos Q−. (shrink)

Aristotle is generally accepted as the father of logic. The ideas that he raised in his study of logical reasoning carried the development of science over the centuries. Today, in the era of AI, this title of the fatherhood of logic has a renewed significance. Behind it lies his original idea that human reasoning could be studied as a process and that perhaps there exist universal systems of reasoning that underlay all human reasoning irrespective of the content of what we (...) are reasoning about. In this article, we look into Aristotle’s work on human thought, his work on reasoning itself but also on how it relates to science and human endeavor more generally, from a modern perspective of Artificial Intelligence and ask if this can help enlighten our understanding of AI and Science more generally. Could Aristotle enlighten us to a new path of understanding the human capacity to think, that would allow a natural non-polluting development of AI that can energize and expand human thought into new horizons? (shrink)

The paper examines the interplay of classical concept theory, Buddhist philosophy, and Russian metaphysics, focusing on the inverse relationship between a concept’s content and extension. It shows that a concept with infinite content, including contradictory attributes, has a null extension, making it “empty.” This is interpreted through Buddhist śūnyatā (Madhyamaka, Diamond Sutra) and linked to Solovyov’s “all-unity” and Florensky’s “antinomy.” Using non-classical logic (dialectical, multi-valued, quantum), it establishes the equivalence of “everything” and “nothing.” The analysis connects these ideas across philosophical (...) traditions and highlights their relevance to modern science, including ecology, AI, and complex systems. (shrink)

This paper explores an alternative non-relational semantics for modal logic, framing modal systems as "poly-logics"—intersections of simpler, foundational logics. Building on pioneering work by J. Kearns and subsequent developments, we demonstrate how established systems such as K series (K, K4, K5, K45), KD series (KD, KD4, KD5, KD45), KB series (KDB, KB, KB4, KB5, KB45) emerge as intersections of logics like KT, KTB, FN, TR, and their extensions. Utilizing Resolution Matrix Semantics (RMS), we establish soundness and completeness for key systems (...) with sketched proofs and introduce an innovative tableau-based proof procedure tailored to RMS. This approach not only unifies disparate modal frameworks but also yields efficient algorithmic tools for validity checking, offering fresh insights into the algebraic structure of modal deduction. Examples illustrate the method's efficacy, highlighting its advantages over traditional Kripke-style model checking. (shrink)

This paper argues that the contrast between “something” and “nothing” fails before explanation begins: absolute nothingness is not a failed rival to actuality, but never qualifies as a rival at all. The argument requires no necessary being, no privileged inventory of existents, and no particular modal logic. Nor does it begin from intuitions about empty worlds or from the claim that we cannot imagine “nothing.” It turns instead on a prior question: what must be in place for a candidate to (...) count as an alternative? That condition is the Structure-Base Principle (SBP): determinacy cannot outrun being. Whenever a claim or scenario is treated as a genuine alternative—a candidate that could be true rather than false, or obtain rather than fail to obtain—some determinacy-enabling structure already obtains. This is not about minds, language, or representation; it concerns objective conditions of determinacy that would obtain even in a mindless, language-less cosmos. Ordinary absence poses no problem: a room can contain no chairs, a region no electrons, a model no objects in its domain. But such absences are determinate only relative to a contrast-field. Absolute nothingness is different: it is the alleged cancellation of every such field. The proposed alternative therefore fails in either reading: read as a state, absolute nothingness makes something the case while requiring that nothing be the case; read as a bare denial, it leaves no candidate alternative to actuality. Attempts to place nothingness at a world, region, or void reintroduce the backdrop they deny. Because the point concerns determinacy itself, not proof-system choice, the paper argues that the result is invariant across classical, free, intuitionistic, relevant, and paraconsistent logics. More radically than a square circle or married bachelor, absolute nothingness is not even an impossible configuration but rather the attempted cancellation of configuration itself. (shrink)

By extending the notion of a Well Formed Formula to include syntactically formalized rules for rejecting semantically incorrect expressions we recognize and reject expressions that have the semantic error of Pathological self-reference(Olcott 2004). The foundation of this system requires the notion of a BaseFact that anchors the semantic notions of True and False. When-so-ever a formal proof from BaseFacts of language L to a closed WFF X or ~X of language L does not exist X is decided to be semantically (...) incorrect. (shrink)

Ontological arguments like those of Gödel (1995) and Pruss (2009; 2012) rely on premises that initially seem plausible, but on closer scrutiny are not. The premises have modal import that is required for the arguments but is not immediately grasped on inspection, and which ultimately undermines the simpler logical intuitions that make the premises seem plausible. Furthermore, the notion of necessity that they involve goes unspecified, and yet must go beyond standard varieties of logical necessity. This leaves us little reason (...) to believe the premises, while their implausible existential import gives us good reason not to. (shrink)

Motivated by the urgency of making explicit “the laws of possible rational passage from one concept to another”, which Professor F. William Lawvere brought into figural salience for all to see and work on, here I present my research proposal entitled Bhāvana Adhyayanaṁ, the main objective of which is: (i) characterize the space of concepts and (ii) derive laws governing the passage between concepts based on the space of concepts.

Large language models have demonstrated notable performance across various logical reasoning benchmarks. However, it remains unclear which core logical skills they truly master. To address this, we introduce LogicSkills, a unified benchmark designed to isolate three fundamental skills in formal reasoning: (i) formal symbolization—translating premises into first-order logic; (ii) countermodel construction—formulating a finite structure in which all premises are true while the conclusion is false; and (iii) validity assessment—deciding whether a conclusion follows from a given set of premises. Items are (...) drawn from the two-variable fragment of first-order logic (without identity) and are presented in both natural English and a Carroll-style language with nonce words. All examples are verified for correctness and non-triviality using the SMT solver Z3. Across leading models, performance is high on validity but substantially lower on symbolization and countermodel construction, suggesting reliance on surface-level patterns rather than genuine symbolic or rule-based reasoning. (shrink)

In this article, we provide three generators of propositional formulae for arbitrary languages, which uniformly sample three different formulae spaces. They take the same three parameters as input, namely, a desired depth, a set of atomics and a set of logical constants (with specified arities). The first generator returns formulae of exactly the given depth, using all or some of the propositional letters. The second does the same but samples up-to the given depth. The third generator outputs formulae with exactly (...) the desired depth and all the atomics in the set. To make the generators uniform (i.e. to make them return every formula in their space with the same probability), we will prove various cardinality results about those spaces. (shrink)

Un libro de texto de lógica, argumentación y razonamiento probabilístico que he estado escribiendo durante los últimos años. Lo he usado para clases en bachillerato, licenciatura y posgrado. Está incompleto todavía, pero las primeras tres partes (argumentación, lógica proposicional, y cuantificación) están completas a un 85%, aproximadamente. Si lo usas, me ayudarías mucho mandándome comentarios, críticas y cualquier sugerencia.

This book aims to be efficiently and succinctly comprehensive in covering the categorical logic, propositional logic, predicate logic, and modal logic areas of classical logic, with a chapter at the end on how classical logic can relate to theories of knowledge and knowledge itself. Kendall Hunt, Inc./Innovative Ink Publishing.

Artificial Intelligence, in press. Abstract: For some time we have been developing, and have had significant practical success with, a time-sensitive, contradiction-tolerant logical reasoning engine called the active logic machine (ALMA). The current paper details a semantics for a general version of the underlying logical formalism, active logic. Central to active logic are special rules controlling the inheritance of beliefs in general (and of beliefs about the current time in particular), very tight controls on what can be derived from direct (...) contradictions (P &￢P), and mechanisms allowing an agent to represent and reason about its own beliefs and past reasoning. Furthermore, inspired by the notion that until an agent notices that a set of beliefs is contradictory, that set seems consistent (and the agent therefore reasons with it as if it were consistent), we introduce an “apperception function” that represents an agent’s limited awareness of its own beliefs, and serves to modify inconsistent belief sets so as to yield consistent sets. Using these ideas, we introduce a new definition of logical consequence in the context of active logic, as well as a new definition of soundness such that, when reasoning with consistent premises, all classically sound rules remain sound in our new sense. However, not everything that is classically sound remains sound in our sense, for by classical definitions, all rules with contradictory premises are vacuously sound, whereas in active logic not everything follows from a contradiction. (shrink)

Which premisses should we use to start our inquiries? Which transitions during inquiry should we take next? When should we switch lines of inquiry? In this paper, I address these open questions about inquiry, formulating novel norms for such decisions during deductive reasoning. I use the first-order predicate calculus, in combination with Carnap’s state description framework, to state such norms. Using that framework, I first demonstrate some properties of sets of sentences used in deduction. I then state some norms for (...) decisions made during deductive reasoning, establishing initial benchmarks for efficient deduction by ideal reasoners. When deciding which transition to make next, reasoners should choose the most informative transition, the one that maximally reduces uncertainty in the sense of ruling out the largest number of state descriptions relevant to their inquiry. Finally, inspired by optimal foraging theory, I show that, under certain assumptions of ignorance, reasoners should change premiss sets when their information intake drops below the global average information intake across premiss sets. (shrink)

This chapter focuses on formalizing understood as the practice of assigning formulas to ordinary-language arguments and sentences with the aim of representing logical forms transparently and making it possible to give formal proofs and theoretically respectable explanations of validity. This practice raises the question of how the adequacy of formalizations can be assessed. The relatively few attempts at explicating criteria of adequacy for formalizations have mostly focused on two ideas. Either formalizations are required to correctly represent inferential properties of sentences, (...) or they are expected to correspond to sentences with respect to truth-conditional structure. This chapter analyses how such criteria function, what presuppositions they rest on, and what their limitations and problems are. Issues raised by equivalent sentences and equivalent formalizations show that these criteria still permit formalizations that lead to unnecessarily trivial or wrong explanations of validity. What is missing is that adequate formalizations must be the result of assigning formulas to sentences in a systematic way. This links criteria of adequacy to compositionality and procedures of formalizing. (shrink)

A logic is said to be hyperintensional when it admits connectives or operators creating hyperintensional contexts, i.e. sentential contexts not respecting the intersubstitutivity salva veritate of co-intensionals. Odintsov and Wansing (2021) suggest a formal criterion for classifying a logic as hyperintensional based on whether its consequence relation is self-extensional. I argue that satisfaction of Odintsov and Wansing's criterion is neither necessary nor sufficient for characterising a logic as hyperintensional. Indeed, the criterion classifies as hyperintensional logics which are not meant to (...) capture hyperintensional behaviour, and fails to classify as hyperintensional logics which admit some forms of hyperintensional behaviour. I suggest several possible criteria for a logic to count as hyperintensional, arguing that each of them corresponds to a different understanding of hyperintensionality for logics. Then, I weigh these criteria against a family of logics, which display different "nuances'' of hyperintensional behaviour. Finally, I gesture towards a diagnosis of hyperintensionality for logics. (shrink)

This paper offers a formal and exegetical analysis of the notion of proprium (proper accident), a concept rooted in Aristotelian logic and further developed by Thomas Aquinas and other medievals. While commonly defined as a property that necessarily follows from a thing’s essence without being part of it, the proprium has been a source of terminological divergence and substantive disagreement, both in scholastic and analytic circles. We defend a refined version of Kit Fine’s account—according to which propria follow logically from (...) essence—by situating it within the framework of Aristotelian-Thomistic logic and explicating it through higher-order logic. In particular, we argue that proper accidents are those whose definition contains the proper subject as a specific difference, thus violating the so-called “inverse proportion of extension and comprehension,” and yielding propositions that are true solely in virtue of the meaning of the terms involved, while being non-analytic in a modern sense. The paper contributes both a formal reconstruction of the concept and a historical reinterpretation of Aquinas’s position, and it clarifies how our account refines or reconciles competing contemporary views—especially those framed in causal rather than logical terms. (shrink)

In this article I offer an explicating interpretation of the procedure of content recarving as described by Frege in §64 of the Foundations of Arithmetic. I argue that the procedure of content recarving may be interpreted as an operation that while restricting the subject matter of a sentence, performs a generalization on what the sentence says about its subject matter. The characterization of the recarving operation is given in the setting of Yablo’s theory of subject matter and it is based (...) on the relation of determination between properties. The main advantage of the proposal is its generality, for it is applicable not just to the case of abstraction principles. (shrink)

The pivotal problem any interpretation of Cartesian modality has to cope with is how to reconcile Descartes's claim that God freely created the eternal truths with his contention that the eternal truths are necessarily true. In this article, the author argues for a Frankfurt-style solution to the puzzle, according to which Cartesian divine free agency does not require the ability to do otherwise.

Logical contextualism is the view that ‘valid’ is a context-sensitive expression. An often-invoked motivation for this view is that, unlike traditional forms of logical pluralism, it appears to avoid the so-called collapse problem. In this paper, I argue for a twofold conclusion. First, I argue that the key tenets of logical contextualism require further development before the view can be fully assessed. Second, I argue that, even if we set this issue aside, logical contextualism rests on an untenable assumption: that (...) each context determines a unique logical consequence relation. I then show that, once this assumption is rejected, logical contextualism’s solution to the collapse problem is unsatisfactory. My overarching conclusion will be that logical contextualism is a less promising view than thus far appreciated. (shrink)

In contemporary philosophy there is much focus on conceptual engineering: the enterprise of revising and replacing concepts. In this talk, I focus on a theoretical issue that has not yet received much attention. What principled limits are there to this sort of enterprise? Are there concepts that for principled reasons cannot or should not be revised or replaced? Examples discussed include logical concepts and normative concepts.

In this chapter, we consider the question in what sense (if any) logic is normative. We first provide an opinionated overview of the recent debate (Part I), and then we put forward a proposal on which logic is intrinsically normative (Part II). Settling whether logic is normative seems to presuppose answers to: (a) What is logic? (b) What is it (for logic) to be normative?

The paper “Tautology elimination, cut elimination, and S5” published in this journal presents a novel method for establishing by proof analysis the admissibility of the rule of tautology elimination for certain sequent calculi. Since tautology elimination will typically imply the admissibility of cut, the method promises a new path to show the admissibility of cut for cut-free calculi on which the standard techniques within structural proof theory seem inapplicable. This paper shows that the method as presented involves an error.

In a paper published in this journal, Golan argues for the thesis that there is no tenable notion of global metainferential validity. The conclusion rests on the premise that metainferential validity for propositional languages should be closed under uniform substitution of arbitrary formulas for atoms. This paper looks into Golan's justification for this premise in terms of the formality of logic. It is argued that neither formality as schematicity nor formality as topic-neutrality implies closure under uniform substitution of arbitrary formulas (...) for atoms as requirement. It is also argued that the justification of such a requirement in terms of the formality of logic makes Golan's conclusion irrelevant for logical research. (shrink)

In this paper, I distinguish and compare three kinds of logical expressivism. The first, reminiscent of attitude expressivism in meta-ethics, holds that logic is expressive in that logical vocabulary serves to express attitudes. For instance, traditional attitude expressivism about negation, going back to the work of Frank Plumpton Ramsey, Huw Price and others, holds that 'not' expresses disbelief. The second kind of logical expressivism, reminiscent of deflationism about truth and championed by Robert Brandom, holds that logic is expressive in that (...) logical vocabulary serves to make explicit—typically, by expressing them as contents of assertions—the commitments that are implicit in our discursive practices. For instance, content expressivism about the conditional holds that 'if' expresses as content commitment to the goodness of certain inferential moves. The third kind of logical expressivism, and the one I will be arguing for, holds that, in a sense, logic is expressive in both ways: logical vocabulary serves to make explicit commitments to expressions of attitudes. (shrink)

In her seminal article `Proper Classes', Penelope Maddy introduced a novel theory of classes validating the naïve comprehension rules. The theory is based on a step-by-step construction of the extension and anti-extension of the membership predicate, which mirrors Kripke's construction of the extension and anti-extension of the truth predicate. Maddy's theory has been criticized by Øystein Linnebo for its 'rampant indeterminacy' and for making identity among classes too fine-grained. In this paper, I present a theory of classes which, while building (...) on Maddy's theory, avoids its rampant indeterminacy and allows for identity among classes to be suitably coarse-grained. I begin by presenting a bilateral natural deduction system for Maddy's theory, which improves on her axiomatization in several respects. I then go on to show how to avoid the rampant indeterminacy by using supervaluational schemes in the construction of the extension and anti-extension of the membership predicate and how to augment the proof theory with corresponding, motivated rules. It turns out that whilst a van Fraassen-style supervaluational scheme suffices to avoid the basic problem of rampant indeterminacy, a supervaluational scheme based on maximally consistent extensions is needed for a proper treatment of identity. (shrink)

We demonstrate that, in itself and in the absence of extra premises, the following argument scheme is fallacious: The sentence A says about itself that it has a certain property F, and A does in fact have the property F; therefore A is true. We then examine an argument of this form in Gödel's introduction to his classic paper on incompleteness and examine some auxiliary premises which might have been at work in that context. Philosophically significant as it may be, (...) that particular informal argument plays no rôle in Gödel's technical results. Going deeper into the issue and investigating truth conditions of Gödelian sentences (i.e. those sentences which are provably equivalent to their own unprovability) will provide us with insights regarding the philosophical debate on the truth of Gödelian sentences of systems – a debate which goes back at least to Dummett in the 1960s. (shrink)

The article recapitulates what logic is about traditionally and works out two roles it has been playing in philosophy: the role of an instrument and of a philosophical discipline in its own right. Using Tarski’s philosophical-logical work as case study, it develops a logical reconstructionist methodology of philosophical logic that extends and refines Rudolf Carnap’s account of explication and rational reconstruction. The methodology overlaps with, but also partially diverges from, contemporary anti-exceptionalism about logic.

Modal Interpretations of quantum mechanics distinguish between the realm of possibility, where the dynamical state determines what may be the case, and the realm of actuality, where the value state represents what actually is the case. In particular, the Modal-Hamiltonian Interpretation proposes an ontology in which there are no individual objects: quantum systems are characterized as non-individual bundles of properties. The aim of the present paper is to propose some first steps towards the development of a new modal logic adapted (...) to describe a possibilist modality in an ontology of properties. The main idea consists in conceiving possibility as fundamental and introducing actuality as an operator acting on possible facts. On this basis, propositions referring to possible facts and propositions referring to actual facts are distinguished, and some relations between the realm of possibility and the realm of actuality are introduced. (shrink)

In reasoning, we draw conclusions from multiple premises. But thinkers can be fragmented. And if there is no single fragment of the agent that thinks all of the premises, then the agent cannot draw any conclusions from them. It follows that reasoning from multiple premises depends on their being thought together. But what is it to think premises together? What is the condition that contrasts with fragmentation? This paper provides an answer to this question that is simple but compelling: to (...) think premises together is to attribute those very thoughts to one and the same self. The ability to reason depends on the ability to attribute the thoughts from which one reasons to oneself. Reasoning—at least the sort of reasoning that we do—requires de se thought. (shrink)

The most serious objection to Beall and Restall’s case-based logical pluralism is the so-called collapse argument. According to the collapse argument, logical pluralism is not genuinely pluralistic and collapses into a single privileged relation of logical consequence. In response, Caret offered an account of logical contextualism that supposedly maintains the merits of Beall and Restall’s case-based logical pluralism while circumventing the collapse argument. In this paper, I first point out a gap in the collapse argument in that it does not (...) affect pluralists who assume that there is no uniquely strongest admissible consequence relation. This gap, then, is closed by an improved version of the collapse argument, which makes use of Eklund’s classification of types of pluralism. Finally, I discuss how Caret’s logical contextualism cannot hold up against this new formulation of the collapse argument unless implausible assumptions about the contents of normative operators are made. Moreover, by reformulating the collapse argument, I determine the extent to which logical monism and pluralism oppose each other, paving the way for fruitful future discussion. (shrink)

The usual approach to validity holds that an argument is valid in virtue of its form. This idea has been developed along two main lines: model-theoretic and proof-theoretic. Both frameworks presuppose a distinction between logical and non-logical vocabulary. This chapter introduces these two conceptions of validity and discusses their respective approaches to the demarcation question. We review two versions of the overgeneration challenge for the model-theoretic account, formulated in terms of isomorphism invariance. Similarly, we review two challenges faced by the (...) proof-theoretic account, formulated in terms of the logical vocabulary’s inferential role. The chapter thus offers a comparative overview of the model-theoretic and proof-theoretic conceptions of formal validity. (shrink)

If validity, consequence, and related notions comprise the subject matter of logic then, intuitively, logics should provide us with explanations when those concepts are involved. On this view, a model theory might be seen as explaining why there is no way to make the premises true and conclusion false. However logical explanation, like mathematical explanation, does not fit easily into standard theories of explanation. In this chapter we give an overview of arguments for and against the claim that logics explain, (...) survey the theories of explanation in relation to logic, and discuss the role of modelling in logical explanation. We also consider the relationship(s) between accounts of logical explanation and debates about the epistemic status of logic, and explore the tension between the descriptive goal of explanations and the traditional normative role of logic. (shrink)

This paper examines Venn diagrams as a case study in visual representation. Venn diagrams have a clear formal structure and well-defined correctness conditions. The central question is whether they possess a recursive syntax and corresponding compositional semantics analogous to those developed for formal and natural languages. Existing research notably fails to provide a compositional semantics for Venn diagrams. This may suggest a fundamental divide between linguistic and visual representation, or instead a case of representation that resists compositional analysis. The paper (...) presents two approaches to the syntax of Venn diagrams—a region-first approach and a cell-first approach—and develops a compositional semantics for each. In doing so, it clarifies the similarities and differences between linguistic representation and diagrammatic representation, and it suggests new avenues for interpreting other forms of visual representation. (shrink)

This is to appear in a Festschrift for Hilary Putnam on his 85th birthday. This is a pre-publication, not final, version.

We present a construction of nondeterministic semantics for some deontic logics based on the class of paraconsistent logics known as Logics of Formal Inconsistency (LFIs), for the first time combining swap structures and Kripke models through the novel notion of swap Kripke models. We start by making use of Nmatrices to characterize systems based on LFIs that do not satisfy axiom (cl), while turning to RNmatrices when the latter is considered in the underlying LFIs. This paper also presents, for the (...) first time, a full axiomatization and a semantics for the CDn hierarchy, utilizing the aforementioned mixed semantics with RN matrices. It includes the historical system CD1 of da Costa and Carnielli (1986), the first deontic paraconsistent system proposed in the literature. (shrink)